Discussion

The Pearson Linear correlation coefficient (r) for the following paired data (x, y) : (2, 1.4) (4, 1.8), (8, 2.1), (8, 2.3), (9, 2.6) is

Answer: C

The Pearson correlation is the covariance of x and y divided by the product of their spreads. The means are 6.2 for x and 2.04 for y.

\[ r = \frac{S_{xy}}{\sqrt{S_{xx} S_{yy}}} \]

\[ S_{xy} = \sum (x - \bar{x})(y - \bar{y}) \]

\[ r \approx 0.957 \]

So the answer is 0.957, option C. A negative value is impossible as y rises with x.

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